Minecraft render animation skin not working
Without the original blend file I can only think that:

The template model is using a custom unwrap texture*.
Your skin is a custom skin*.

*not following the minecraft uv or model uv setup.
Download the original steve skin, replace the templet skin with the steve one, select the model, go to edition mode with the UV editor open on one window, select all the vertex and look if the unwrap is well done.